Quantitative chemical analysis by x-ray emission spectroscopy

ABSTRACT

In X-ray emission spectrometry a quantitative chemical analysis of the elements in an unknown sample is obtained. A standard, or standards, whose composition has previously been accurately established is used to determine the first order approximation to the original intensity of the most efficient excitation energy for each element being determined. The most efficient excitation energy is defined as that energy which is just greater than the energy of the absorption edge of the characteristic X-ray emission line employed in the analysis. Using the computed original intensity of the most efficient excitation energy for each element in the standard(s), the observed X-ray intensities measured on the unknown, and an assumed chemical composition of the unknown, the expected characteristic X-ray intensity for each element in the unknown is computed. The assumed chemical composition of the unknown is then adjusted by a self-consistent iterative procedure until the expected and observed X-ray intensities for each element being determined agree. In this manner the best estimate of the chemical composition of the unknown is determined.

United States Patent Q [1 1 3,703,726

Stephenson 1 Nov. 21, 1972 [54] QUANTITATIVE CHEMICAL Primary Examiner-Charles E. Atkinson ANALYSIS BY X-RAY EMISSION Assistant Examiner-Jerry Smith SPECTROSCOPY Attorney-Clarence R. Patty, .lr., Walter Zebrowski [72] Inventor: nald A; Stephenson, Corning, and woodcckwas'hbumjumac Mack'ew'cz N Y [571 ABSTRACT [73] Asslgnee: 5 works In X-ray emission spectrometry a quantitative chemiical analysis of the elements in an unknown sample is [22] Filed: Dec. 31,1970 iobtained. A standard, or standards, whose composiition has previously been accurately established is used Appl ml {to determine the first order approximation to the v original intensity of the most efficient excitation ener- [52] US. Cl. ..444/1, 235/ 151.3, 235/151.35., .8) for each element being determined. The most effi- 250/515 cient excitation energy is defined as that energy which [51] Int. Cl. ..G06l /46 is ju t greater than the energy of the absorption edge Field Selrfllb235/ 1, -1 1 1- 151 5; of the characteristic X-ray emission line employed in 2 0/4l-9 R, 51-5, R, l 'the analysis. Using the computed original intensity of the most efficient excitation energy for each element References Cited l in the standard(s), the observed X-ray intensities meaf sured on the unknown, and an assumed chemical com- UNXTED STATES PATENTS %position of the unknown, the expected characteristic 3,581,087 5/1971 Brinkerhoff et a1. .....250/5l.5 IX-ray intensity for each element in the unknown is 3,537,820 11/1970 Markant et al. ..235/ 151.12 X 3 computed. The assumed chemical composition of the ,108 7/1969 Pichoir; ..250/51.5 X unknown is then adjusted by a self-consistent iterative 3,428,802 2/1969 Mehta et a1 .250/51.5 procedure until the expected and observed X-ray in- 0 7 8/1971 Vamela ..235/l5l-l2 X tensities for each element being determined agree. In 3,553,444 l/l971 Tong ..235/151.35 this manner the best estimate of the chemical composition of the unknown is determined.

M r i;LE a1m 1PM"?! Figures W1 1i? KEE T DATA FOR m: STANOARDlS) cTfcu CKTE a a LOOK or ALL use-J can" cosmeeucuum mensv or near uric-j" non EACH r I EXCITA ENERGY FOR L H N mPur ALL run 24 son THE J ummowms) CALCULATE INITIAL ASSUIAED CONPOSI- r25 HON OF THE NKNOWN (3) CAL CU LATE E2 PFC- a ummowu (s) ESTIMATE EXPECTED INTEN- OF ASSUME]; SITIES OF EACH COMPOSITION ELEMENT AGREE gum: camas mm or 1: J

PNENTED m 1 12 3. 703'. 72s

SHEET 1 BF 2 l2 SAMPLE CRYSTAL PRE- :6 DETECTOR AMP AMP PULSE HEIGH T J- SELECTOR SCALER I90 .1 DIGITAL COMPUTER} PIITENTEDmm m2 Sum 2 OF z 7 DATA INPUT. ALL

FOR

THE STAND'A RD (S) CALCULATE OR- LOOK UP ALL NEC- 'ESSARY COEFFIC- ELE MENT INPUT ALL DATA FOR THE- UNKNOWN IS) CALCULATE INITIAL ASSUMED COMPOSI- TION OF THE 7 UNKNOWN (s) CALCULATE EXPEC- TED X-RAY INTEN- SIT-IE5 OF EACH ELEMENT IN UNKNOWN (S) CALCULATE NEXT ESTIMATE OF ASS UM ED COMPOSITION I DO OBSERVED AND EXPECTED INTEN- SITIES OF EACH ELEMENT AGREE OUTPUT COMPO SITION OF THE UNKNOWNISI BACKGROUND OF THE INVENTION This invention relates to X-ray emission spectrometry and more particularly to the quantitative chemical analysis of a sample based on the theoretical interpretation of X-ray emission spectra.

Methods of X-ray detection have been improved so that it is now a simple routine to accurately measure relative X-ray intensities. X-ray spectrometry is now extensively used in both quantitative and qualitative chemical analysis. X-ray Absorption and Emission in Analytical Chemistry, Liebhafsky, Pfeifier, Winslow and Zemany, 1969, John Wiley & Sons, lnc., describes techniques of X-ray emission analysis.

The advent of the general purpose digital computer has enabled many X-ray emission analyses to be performed which previously were impractical because of the burdensome number of calculations or table lookups to be performed. One such use of a digital computer to perform a qualitative analysis from X-ray emission data was made by Mr. Frank Chambers, IBM Corporation and demonstrated at the Conference on Analytical Chemistry, Pittsburg, Pennsylvania, 1968. J. W. Criss and L. S. Birks in Volume 40 of Analytical Chemistry describe the use of digital computers to perform quantitative X-ray emission analysis by different techniques.

Previous theoretical treatments of X-ray emission data for quantitative analysis described by J. W. Criss and L. S. Birks in Volume 40 of Analytical Chemistry and by T. Shiraiwa and N. Fujino in Volume 5 of the Japanese Journal of Applied Physics have been impractical because they require a detailed knowledge of the spectral distribution of the X-ray tube used to excite characteristic X-ray spectra of the elements contained in the analyzed sample. This information is quite difficult to accurately obtain and the corresponding correction calculations are more complex.

SUMMARY OF THE INVENTION In accordance with an important aspect of this invention a single most efficient X-ray excitation energy for each element in a sample is defined. This energy is just greater than the X-ray absorption edge of the characteristic X-ray emission line of the element being determined. Using a first order approximation of the intensity of the most eflicient energy obtained from standards, the expected X-ray intensity for each element in the unknown is computed based upon an assumed chemical composition. This expected X-ray intensity is then compared with the observed intensity for that element. Using a self-consistent iterative procedure the weight percents of the elements in the unknown are adjusted so that the observed and calculated X-ray intensities agree. When the observed and calculated X-ray emis sion intensities coincide, the adjusted weight percents of the elements are the best estimates of the chemical composition of the sample.

This technique of assuming a single X-ray excitation energy and using the inverse self-consistent iterative adjustment procedure to perform a quantitative analysis is less complex than performing a quantitative analysis based upon a detailed knowledge of the spectral distribution of the X-ray tube used to excite the elements.

It has the advantage of being performed completely automatically in a very short time and with accuracy comparable to that of wet chemical analysis.

DESCRIPTION OF THE DRAWINGS FIG. 1 shows a block diagram of typical X-ray emission measurement system;

FIG. 2 is a flow sheet depicting the process of this invention.

DESCRIPTION OF A PARTICULAR EMBODIMENT FIG. 1 depicts an X-ray emission spectrometric system which is typical of but not limiting of the system's to which the present invention is applicable. It will be appreciated that this invention is also applicable to similar analytical techniques which produce X-rays for the examination of materials.

In the X-ray emission spectrometer, a chromium or tungsten target X-ray tube is commonly used for the X- ray source 11. Radionuclides may also be used. X-rays from this source irradiate the sample 12 at an angle of incidence 0 Excitation of each element in the sample produces characteristic X-rays observed at an angle 0 The emitted radiation is collimated by the collimator 13. An analyzing crystal l4 resolves the emitted spectrum which is again collimated by a collimator 15.

The intensity measurement system includes an X-ray detector 16 producing pulses proportional in number and energy to the emitted X-ray photons. These pulses are amplified and shaped by preamplifier 17 and amplifier 18 to provide a useful signal. A pulse height selector 19 selects pulses of appropriate energy to be counted and rejects others. The pulses are counted by a scaler or similar electronic counter for an appropriate time and these data are suitable for input to a digital computer 20.

Systems of the type described with reference to FIG. 1 have been used quite successfully for the identification of elements in a sample, i.e., qualitative analysis, andfor quantitative analysis based on techniques different than those described herein. While the intensity of each X-ray line is related to the amount of each element in the sample, the relationship is complicated, and variations in the characteristics of the X-ray source 1 l affect the observed intensities.

In accordance with the present invention it is not necessary to precisely determine the characteristics of the X-ray source. Rather, it is assumed that the X-rays which irradiate the sample are monochromatic and have an energy which is just slightly greater than the X- ray absorption edge of the characteristic X-ray emission line of each element in question.

Absorption edges, or critical absorption energies, are discussed more fully in the aforementioned text X-Ray Absorption and Emission in Analytical Chemistry, page 16. For the simplified purposes of this discussion, the Xray absorption edge is the critical energy necessary to expel an electron from the particular energy level responsible for the production of characteristic X-rays of each element in the sample.

As an example, assume there is a known mixture (standard) of elements A and B. This mixture is irradiated to obtain a measurement of the Km; X-ray emission line of both elements. In accordance with this invention it is assumed that the energies of the incident X-rays which produced each line are just above the K absorption edge of each line. Under this assumption, Ka X-rays are emitted most efiiciently. The step of irradiating the sample and gathering the intensity data is indicated at step 21 in the flow sheet of FIG. 2 which depicts the invention.

With the aforementioned assumption, the intensity of the most efficient excitation energy for each element can be computed. This step is indicated at step 23 in the flow sheet. The computation is carried out in ac cordance with where If is the first order approximation of the intensity of the most efficient excitation energy of the ith element,

1, is the observed X-ray intensity for the ith element,

is the angle of incidence of the irradiating energy,

6 is the angle at which characteristic X-rays are observed,

t," is the mass absorption coefficient of the sample for the most efficient X-rays,

,u, is the mass absorption coefiicient of the sample for the ith radiation,

u, is the mass absorption coefficient of the ith element for the most efficient X-rays,

W, is the weight fraction of element 1',

K, is the absorption edge jump ratio for the ith element,

0, is the fluorescent yield of the ith element, and

R is the fraction of the characteristic X-rays in the analyzed lines series.

The foregoing coefficients are all well-defined in X- ray spectrometry. The calculation of, or table look-up of, these coefficients are indicated by step 22 of the flow sheet. A few brief comments on these coefiicients will be helpful. The weight fraction of each element W, is the decimal fraction which varies between 0. and l. The fluorescent yield 0, is the efiiciency with which X- rays are produced relative to auger electrons.- When a K electron is ejected, another electron takes its place. However, instead of emitting X-rays, an electron may be ejected from the excited atom. When the probability of electron ejection is high there is not a high yield of X-rays. The fluorescent yield of the element, (1,, is described more fully on page 36 of the aforementioned text. The fraction R, can best be explained with reference to an example. For aluminum, there are two principal K lines, aluminum Ka and aluminum K6,.

tion of X-rays in the Ka line relative to the total number of X-rays in the K emission series for aluminum. The mass absorption coefficients 1.1,", p4,, and M are a measure of the probability that an X-ray of energy P will be absorbed by the sample, an X-ray of energy i will be absorbed by the sample, and an X-ray of energy P will be absorbed by the ith element respectively. These data are readily available.

The absorption edge jump ratio K is a measure of the fraction of X-ray energy absorbed by element i that is responsible for the ejection of electrons from the energy level connected with the observed characteristic X- rays. In this example, assume that the sample is 20% A, therefore the weight fraction W is 0.20 and W, is 0.80.

The computation just performed at step 23 in the flow sheet in accordance with equation (l) will produce the intensity of the most efficient excitation energy for element A. This computed value is used in equation (2) given below, in conjunction with an assumed composition of the unknown (step 25) to compute the expected X-ray intensity If for element A in the unknown.

where the remaining symbols are as previously defined. This calculated intensity 1 is compared with the observed intensity I,,. Then, the weight fraction W, of element A in equation (2) is adjusted by an iterative procedure (steps 26, 27, and 28) until 1 matches I When this is obtained the value of W is the best estimate of the weight fraction of element A. The same procedure is followed penecontemporaneously to obtain the weight fraction of element B. iterative adjustment of elements A and B continues until the observed intensities of A and B agree (step 29).

While the invention is useful for simple examples such as that described above it is even more useful for complex mixtures. Its utility is best demonstrated with reference to an actual example of the analysis of four Assuming that Ka is the line of interest, R, is the frac- 13 element mixtures (Table 1).

TABLE 1.COMPARISON OF WET-CHEMIC COMPONENT MIXTURES. VALU AL AND X-RAY EMISSION ANALYSIS OF FOUR 13 ES ARE IN WEIGHT PERCENT OXIDES.

Sample 1 Suniplo 2 Sample 3 Sumpln 4 Compom-nt Wei-chem X-iay Wot-chem X-ruy Wet-chem X-my Wot-chem X-l'ny S10: 72. U2 2. 88 72. 03 2. 05 70. 61 70. 26 73. 30 73. Hi 1.50 1.5!) 0.36 0. 34 3. H 3. 32 1.20 1.23 0. (H5 0.012 0. 17 0.18 0. (ll 0. 01 0. I15 (l. 111 l. 93 4. 97 ll. 40 ll. 3" ll. 06 10.90 8. .20 8. 1!] 3. 47 3. 41 L. 35 2.. 2X 0. 3-] U. 35 3. l0 3. 37 16. 54 lb. 4!! I3. 35 13.31 12. ll] H. 15 13.40 13.28 0. '2 0. 33 0. 03 0. 02 2. 23 2. 2:: u. 15 0.14 0. 20 0. 20 (I. 33 U. 2!! l]. 1!! l). H! ll. 26 (J. 23 (J. 01 O. 003 0. (ll 0. 005 (I. H 0. ll 0. 0] 0.01 l). (X) 0. 003 0. 00 0. ()U 0. I10 0. 003 0. U0 0. ()0 U. 20 l). 02 0.1!] I). 1!] 0.18 0.13 U, ()2 0.02 U. 03 U. 03 (J. 02 0. U1 0. 03 l). 02 U. 08 0. OH 0. (H 0. 04 I). U. 0. 02 (J. Ul U. ()l 0. 01 U. 01

The analysis produced as accurate results as wet chemical analysis of the mixtures. However, the X-ray spec-.

trometric technique of this invention was performed in approximately 200 seconds per element whereas the, wet chemical analysis requires very much more time tocomplete. Analysis in accordance with this invention can be performed just as fast asall the X-ray intensity measurements can be obtained from the unknown and the standard(s).

Note that the most efficient excitation energy of each element in the samples is slightly greater than the energy of the absorption edge of the measured X-ray emission line of each element. Moreover, any assumed excitation energy greater than the energy tion edge of themeasured X-ray emission line of each element which might be used in this process is within the scope of this invention.

of the absorp,

I elements may be determined by the differencefrom 100 percent, and any number of other analytical techniques, in which case the weight fraction of those elements are employed inthe equations (1) and (2),

but are not alteredin the iterative adjustment procedure.

The use of any coefiicient, parameter, or quantity which is related in a'concise mathematical way to any Not all elements contained in the samples need be determined by X-ray emission techniques. Any one element contained in the samples maybe determined by coefiicient. parameter, or quantity described herein is considered to be identical to the coefficient, parameter, or quantity for the purposes of the computations described herein.

Higher order approximations to the intensity of the most efficient excitation energy may be used and are considered to be within the scope of this invention.

00030 new mass am mama @0060 M090 M mane M: M @0140 @0150 M M172! mmaz @0190 M200 @9210 00220 00230 00240 @2250 @0260 M270 (M266 @0290 Maw @0310 maszu mama M340! M350 @0360 00370 @2382! @0390 054% 0241a @2420: @2430 @044?! 024521 OM60 00470 omao @0490 M500 M510 M522: M530 @0540 massa 0056?! M572 M580 @2590 new COMPUTER ORIENTED X-RAY SPECTROGRAPHIC EMISSION TRANSLATOR r oop ...l... ...l... .I...l. l.l.ll. .....O. .I..... .I..... ...l.l'l. I. Q. I. I. Q. .DIQ... I. .0 .5 l. I. ..l..ll .QQI... l...... G. .IQ'... OQOQ... Q.

A FORTRAN PROGRAM FOR THE THEORETICAL INTERPRETATION OF QUANTITATIVE X'RAY SPECTROGRAPHIC EMISSION DATA ilifiliilii'lllfilll'll...I...OODIOMIOOI...OIDIOOQQOOOlODOQGIIOQII THIS IS THE BATCH ORIENTED VERSION UNIVAC 1108 VERSION LSD RUNS ON IBM/36D BY CHANGING CARDS IN SUBROUTI NES MASARS AND DAD IN 0( I :J) IN ENSI Y FOR I TH COMPONENT AND J TH SAMPLE STDINTI II IS INTENSITY MEASURED ON STANDARD FOR I TH COMPONENT ET O ZERO IF THE ELEMENT HAS NOT DETERMINED BY X' RAY TIME( I o JI COUNTING TIME FOR THE I TH COMPONENT AND J TH SAMPLE ZERO MEANS THE ELEMENT HAS NOT ANALYZEO BY X RAY FONINTI I I PHONEY INTENSITY FOR I TH COMPONENT DETERMINED BY BACK CALCULATION FROM OBSERVED INTENSITY OF I TH COMPONENT. VALID ONLY FOR I TH COMPONENT LINEI I I LINE TYPE ANALI ZED FOR I TH COMPONENT ANALYZEO K ALPHA LINES M ST STOP AT Z 38 CHANGE TO L LINES THIS IS A SUPER CRITICAL REGION. HHEN CHANGING TO LLINES MAKE SURE THE TUBE VOLTAGE IS LONER THAN THE EXCITATION POTENTIAL OF THE K'EDGE OF THE ELEMENT BEING ANALYZED, ERRORS IN THE FLUORESCENCE CORRECTION CAN AND PROBABLY HILL OCCUR IF THIS CONDITION IS NOT MET BECAUSE ABS. COEFFICIENTS ARE UNKNOWN KTUBEI II TUBE TYPE USED TO ANALIZE I TH COMPONENT ASSIGNED I-l SUBROUTINE ASSIGN AS THE KAI. LINE HHOSE ENERGY IS JUST GREATER THAN THE ABS, EDGE OF THE ANALYZED LINE IRRESPECTIVE OF THE ANALYZED LINE '5 SERIES ILINE( I I LINE TYPE USED TO ANALIZE I TH COMPONENT ALHAYS A KAI. LINE IN THIS VERSION AKV( I I TUBE VOLTAGE THETA1 ANGLE OF INCIDENCE THETAZ NGLE AT WHICH INTENSITIES FROM THE SAMPLE ARE MEASURED ICOMP NUMBER OF COMPONENTS ISAMP IS NUMBER OF STANDARDS MUST EQUAL THE NUMBER OF COMPONENTS OR ALL COMPONENTS IS OK IDENTICAL STANDARDS FOR ANY ISKIP EOUAL TO 1 MEANS DO NOT MAKE FLUORESCENCE CORRECTIONS 01280 @1296 @1350 013191 01320 01330 01340 01350 01360 @1370 @1380 @1399 01406 @1410! 0142a @1430 01449 @1450 9514M 01470 @1480 @1490 015% 015.18 @1520 0153B @1540 B1559! B1569 B1570 B1560 B1590 91600 1610 M620 @1630 @1640 @1650 0166B @1670 @1680 016% @1700 6171B @1720 01739! @1746 01750 @1760 017791 01789 01790 018% GOO nnnnul OQOCI O OOOOODOOOOOO CD00 DD 5 K=1| ICOMP CALCULATE MASS ABS, COEFF, OF THE SAMPLE FOR THE PRIMARY X-RAYS AND THE ANALYZED LINES SUM1=SUM1+VALUE(K' I NAMUPEI I |K) SUMZ SUM2VALUEIKI I I'AMUEEI I I o I 0K) CONTINUE ANOTHM IS THE MASS ABS COEFF. OF THE ELEMENT BEING ANALYZED FOR THE PRIMARY RADIATION USED TO ANALYEE IT momnuuu cmn I FORM DIAGIONAL FOR ORIGINAL INTENSITY MATRIX PART1=FACTOR(1, I I'FACTOMZ. I HFACTORIQI, I VALUEI I I I ANOTHM/COSTZ PART2=SUMl/COSTMSUMZ/COSTZ JJJ=IKCNT-1I'KALL*KCNT COEFFIJJJ) =PART1/PART2 CONTINUE KOUNT=-1 DO 8 J=1| ICOMP DO 7 H1. ICOMP TFRCI I )=VALUE( I I J) CONTINUE IF ISKIP.EQ.1) GO TO 8 DD 8 I=1a [COMP IF (J. E. I I GO TO 8 IF (STDINHJ) QEOIQ'U) GO TO 8 KCNT=KCNTv1 CALL FLUCORLJ' I ICOST,-QCOSTZIKOUNTIKALLICOEFFIKCNT) CONTINUE CALL SIMQ(COEFFICCCUKALLO ISING) IF (ISING.E0,1) GO TO 26 DO 9 I=1| ISAMP FONINTI I =w.z

IF (STDINH I I .E0.fl.0) GO TO 9 FONINTI I)=CCC(K) CONTINUE ISAMPL IS THE NUMBER OF SAMPLES BEING ANALYZED IN THIS RUN READ (5-33) ISAMPL READ INTENSITY 0? MASTER STANDATD FOR EACH ELEMENT --STDINT THE INTE SITY OF EACH LINE AND THE COUNTING TIME INTENSITY AND TIME BOTH POSITIVE MEANS THE ELEMENT HAS DETERMINED BY X-RAY MEASUREMENT INTENSITY AND TIME 80TH ZERO MEANS THE ELEMENT IS TO BE DETERMINED Y DIFFERENCE FROM E IGHT FRACTION 1.5

INTENSITY POSITIVE AND TIME ZERO MEANS THE INTENSITY VALUE IS HT, PCT. ELEMENT DETERMINED INDEPENDENTLY 0241:; 02422 @2432 024421 @2450 0246M @2470 02482 024% 525W 02510 @2520 2530 225401 0255a @2560 @2570; 625891 025% 52600 @2610 @2622! 02630 02640 02650 @2660 026m @2680 @2692! @2700 932715 @2720: O273O @2740 @2750 0216a @2770 @2782 02790 @2800 02am 0252a @2830 @2846 @2852: 02am mzem ozsan @2890 @2902! 0291a @2920 02930 @2940 0295a @2960 @2972 0298a @2990 03mm DOUGH Q00 EXRI T I )=(OIPFONINT( I I/COSTZI/OENOH GET IN ENSITY OUE O FLUORESCENT INTERACTIONS IF( ISKIFHEQA.) G O 18 CALL FLUCOFH J: I pCOST1 COST2.KOUNT;KALL,COEFF.Q) CONTINUE BEGIN HYIPERBDLIC APPROXIHATION or uT. FRACTION COMPONENTS DETERMINED av x-mw O 20 I=1| ICOHP IF (TI-MEI I J) 10.9.0) GO TO 70 IF (TINTO( I o J) $0.55 60 TO 19 CONTINUE KO N =KOUN 1 CALL CONC(KOUNT|J) TEST FUR CONVERGENCE KMARK=O DO 21 I=1| ICOMP IFISTOINH I ,EQMJ') GO TO 21 DIFF=ABS(TINTO( I .JI-EXRINTI I 7 I IF (OIFFHLE. .Ofll) GO TO 21 KMARK=1 CONTINUE IF IKOUNLGTJM GO TO 22 IF (KMARIMNEJH GO TO 15 GO TO 3 WRITE (6 37I DO 24 I 1: ICON CALL CAC(SIKOUNT) CONTINUE GO TO 1 RITE (6.38) CALL EXI FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT 'X' 'SINGULAR- MATRIX FOR ORIGINAL INTENSITIES' I FORMATI I1) END SUBROUTINE FLUCDRIJO I I OCOST1ICOSIZQKOUNTOKALLICDEFFIKCNY, ROUTINE TO FIND AND CALCULATE ALL FLUORESCENT INTERACTIONS I X' p HEIGHT FRACTION OF COMPONENTS AFTER ITERATION' 02X, I2)

( 'X' p MORE T AN 10 ITERATIONS SKIPPING TO NEXT SAMPLE I @6742 0675a B6762! 267m mama 06790 msazz 06810 06820 @6830 06842 06852! @6860 06am 06682 @6890 06900 06910 06920 @6932 0694a E6952! E6962! @6972! 069501 06990 07QDE.

(I on on O Q Q n n O DON" GETS INITIAL ESTIMATES OF CONCENTRATON BY LINEAR EXTRAPOLATION OF INTENSITIES NORMALIZES WEIGHT FRACTIONS TO 1 a5 AFTER EACH ITERATION DIMENSION KFLACHZO) COMMON IONE/ TITLE(15) :VALUE(2@.2U)pANAME(2Q);NUMBER(20h HTFRC (20) IIEXRIN'HZZ) 0 WTFRCN(2D) COMMON ITNO/ NGHTUMU),ALIST(1@Q)|LIST(1UU), ISAMP, ICOMP suMA.-.' sun DF PREVIOUSLY DETERMINED ELEMENTS -01 CHANGED SUME, sum or ELEMENTS DETERMINED BY X-RAY sun or ALL wzmm FRACTIONS NORMALIZED T0 1,@

KFLAG NE, 9 MEANS ELEMENT WAS DETERMINED INDEPENDENTLY \l GOOD nnno GO TO 7 ELEMENT IS TO BE DETERMINED BY DIFFERENCE KEY=1 IFLAG=I CONTINUE IF (KEY,EQ.1) GO TO 9 FACT= (1 ,lb-SUMAHSUME 00 8 i=1. ICOMP IF (KT-LAM I .610. 1) GO TO 8 CONTINUE HTFRC( IFLAG) =1 .fD-SUME-SUMA RETURN ENO SUBROUTXNE DTIME DUMMY SUBROUTINE TO BE REPLACED BY USER IF DEADTIME CORRECTIONS ARE NECESSARY COMMON IFIVE/ STDINHZTT). TINTOQT'MZU).TIMUZmZBMFONINHZQ) .FACTO 1 (3.16@ T .LINET20 KTURE 20 TLINET20) .AKWZB) .AHUPE(2U.20 7 ,AMUEE(6 2. 20, 20

RETURN END SUBROUTINE TERMS (MARKTNINLJLINETNAT) CALLED BY MAIN AND FLUCOR DIMENSION JLINEHAZ). NATuw) COMMON IONE/ TITLE 16 7 vALuE(2-'/T.20).ANAME(20).NUMBER(20 T .HTFRC(2D) 1. EXRINT 20 NTFRCNT20) COMMON 7700/ 001171100) .ALlsT(100). 1sT(100 7 TSAMP. xconp COMMON ITHREF/ ENERG1(92) .ENER02T92) .ENERG3(92) |ENERG4(92).ENERG5( 92) .ENER06 92) .ED6E1(92) .EDGE2(92).EOGE3(92) .EOGE4(92) .EDGE5(92 .R 2ATI01(92) .RATT02T92) .RATI03T92) .RATIO4T92) .RATI05192) .NLINEU) .Eoc 3E(2fl).ENERG7(92) COMMON IFIVE/ s nlNflzm TTNTOT20. 20) .TTME 20.20) .FONINNZU) .FACTO 1R(3.160). LTN(20). KTUBE (20) TLTNE 20T .-AKv(20 .ANuPE 20.20) .AMuEE(6 2.20, 20)

so To (1.2). MARK KK=ICOMP KK=NINT+ICOMP 00 T0 (4.5). MARK Z=NUMBER(I) NMBR=NUMBER(I) so To 6 1Z=NAT(I-ICOMP) NNBR=NUMBERH2 K=JLINE(I-ICOMP) FACTOR(3. I IS THE RATIO OF THE INTENSITY OF THE ANALYZED LINE T0 THE TOTAL INTENSITY IN THE EMISSION SERIES 

1. In X-ray emission spectroscopy a method of quantitative chemical analysis of an unknown sample, wherein each of the following computing steps iS performed on automatic computing apparatus, said method comprising: a. irradiating a known standard with X-rays to produce an observed characteristic X-ray intensity from the elements in the standard, b. computing from the observed X-ray intensity of the elements in the standard the first order approximation of the intensity of the most efficient excitation energy for each element, c. computing from said approximations of the intensity of the most efficient excitation energy and an assumed chemical composition of said unknown sample, the expected characteristic X-ray intensity of elements in said sample, and d. adjusting the assumed chemical composition of the unknown sample used in step (c) until said expected X-ray intensities match the observed X-ray intensities of each element in said unknown sample.
 1. In X-ray emission spectroscopy a method of quantitative chemical analysis of an unknown sample, wherein each of the following computing steps iS performed on automatic computing apparatus, said method comprising: a. irradiating a known standard with X-rays to produce an observed characteristic X-ray intensity from the elements in the standard, b. computing from the observed X-ray intensity of the elements in the standard the first order approximation of the intensity of the most efficient excitation energy for each element, c. computing from said approximations of the intensity of the most efficient excitation energy and an assumed chemical composition of said unknown sample, the expected characteristic X-ray intensity of elements in said sample, and d. adjusting the assumed chemical composition of the unknown sample used in step (c) until said expected X-ray intensities match the observed X-ray intensities of each element in said unknown sample.
 2. The method recited in claim 1 wherein the step of computing the first order approximation of the original intensity of the most efficient excitation energy of each element is performed in accordance with: where Ii* is the first order approximation of the intensity of the most efficient excitation energy of the ith element, Ii is the observed X-ray intensity for the ith element, theta 1 is the angle of incidence of the irradiating energy, theta 2 is the angle at which characteristic X-rays are observed, Mu sp is the mass absorption coefficient of the sample for the most efficient X-rays, Mu si is the mass absorption coefficient of the sample for the ith radiation, Mu ip is the mass absorption coefficient of the ith element for the most efficient X-rays, Wi is the weight fraction of element i, Ki is the absorption edge jump ratio for the ith element, Omega i is the fluorescent yield of the ith element, and Ri is the fraction of the characteristic X-rays in the analyzed line''s series. 